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Some L p(L ∞)– and L 2(L 2)– estimates for oscillatory Fourier transforms

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Analysis of Divergence

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

Let \(\begin{gathered} 0 \leqslant {{n}_{k}} \leqslant {{p}_{k}}, 0 \leqslant {{m}_{k}} < {{q}_{k}}, 0 \leqslant {{x}_{k}} < {{p}_{k}},0 \leqslant {{y}_{k}} < {{q}_{k}}, \hfill \\ \left( {{{S}^{a}}f} \right){{\left( t \right)}^{ \wedge }} = {\text{exp}}\left( {it{{{\left| \xi \right|}}^{a}}} \right)\hat{f}\left( \xi \right) \hfill \\ \end{gathered} \). We discuss some examples of maximal estimates and weighted L2-estimates for Sf. The techniques used include asymptotics for Bessel functions and the complete orthogonal decomposition of L2(ℝn) using spherical harmonics.

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Authors
  1. Björn G. Walther
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Editors and Affiliations

  1. Department of Mathematics and Statistics, University of Maine, Orono, ME, 04469, USA

    William O. Bray

  2. Department of Mathematics and Statistics, University of Missouri, Rolla Bldg 202, Rolla, MO, 65409, USA

    Časlav V. Stanojević

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© 1999 Birkhäuser Boston

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Walther, B.G. (1999). Some L p(L ∞)– and L 2(L 2)– estimates for oscillatory Fourier transforms. In: Bray, W.O., Stanojević, Č.V. (eds) Analysis of Divergence. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2236-1_15

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  • DOI: https://doi.org/10.1007/978-1-4612-2236-1_15

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-7467-4

  • Online ISBN: 978-1-4612-2236-1

  • eBook Packages: Springer Book Archive

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